The static envelope of a Gabor patch with a moving carrier appears shifted in the direction of the carrier motion (De Valois & De Valois, 1991). Although several motion processing stages from low to high might contribute to this phenomenon of motion-induced position shift (MIPS), the relationship among the MIPS, binocular disparity, and dichoptically presented carriers, is unclear. To elucidate it, we first investigated the disparity tuning of the MIPS by manipulating the relative disparity between the carrier and envelope. Both a horizontally moving sinusoidal grating inside a Gaussian envelope and the envelope itself had several absolute disparities. The background was filled with static random noise. Two such patches were shown above and below the fixation point, and we determined the point of subjective alignment as the illusion strength. The MIPS occurred even when the moving carrier had radically different disparities than the envelope’s, suggesting that the underlying mechanism of the phenomenon can exist at a monocular visual stage. To confirm this suggestion, in the next experiment we examined whether the depth perception of the envelope was induced by illusory position shifts in interocularly opposite directions. Two Gabor patches moving in opposite directions between the two eyes were presented at the same retinal region. Visible parts of the Gabor patches were horizontally interleaved between the two eyes to exclude depth perception due to an interocular velocity difference between corresponding retinal regions. We found that the depth perception of the binocularly fused envelope of the Gabor patch was biased by the illusory crossed or uncrossed disparity that was expected to occur under the assumption of the MIPS occurrence at a monocular stage. The depth of a similar patch with a hard edged envelope was less biased. We conclude that the position shift is already represented at a monocular processing stage.